EPA-600/2-81-051
August 1981
^91-2J48I7
RESPONSE FACTORS OF VOC ANALYZERS
AT A METER READING OF 10,000 PPMV
FOR SELECTED ORGANIC COMPOUNDS
ly
D.A, DuBose and G,i» Harris
Radian Corporation
P.O. Rax 9948
Austin, Texas 78766
Contract No. 68-02-3171-28
EPA Project Officer: Dr. B.A. Tlchenor
Chemical Processes Branch
EPA/IERL
Research Triangle Park, NC 27711
Prepared for
Office of Air Quality Planning and Standards
-------
TABLE OF CONTENTS
Section * Page
List of Tables . 11
1. INTRODUCTION 1
2. RESULTS . 2
3. DATA ANALYSIS. 12
3.1 Classical Estimation of Response Factors , 12
3.2 Inverse Estimation of Response Factors ......... 14
3.3 Discussion ....... IS
4. LITERATURE REVIEW, . 17
References 24
~
-------
LIST OF TABLES
Number Page
2-1 Response Factors with 95% Confidence Intervals
Estimated at 10,000 ppmv Response 3
2-2 A List of Tested Chemicals which appear to be unable
to Achieve An Instrument Response of 10,000 ppmv
at Any Feasible Concentration 11
ii
-------
SECTION 1
INTRODUCTION
Thir. technical note summarizes the results of a re interpretation of
the data generated in a laboratory study of the sensitivity of two types
or portable hydrocarbon detectors to a variety of organic chemicals. This
work is funded by the EPA as part of Contract Number 68-02-3171, Task 28.
A previous report (Brown, e£ al^ , 1980) presents the description and origi-
nal results of the laboratory study.
The detector sensitivity is quantified by a "response factor" for each
chemical where
Actual Concentration of Chemical
Response Factor = — — —— j — —
Observed Concentration from Detector
The previous report (Brown, et al., 1980) estimated response factors of
10,000 ppmv actual concentration of the chemical. This report presents
response factors estimated for a 10,000 ppmv detector reading.
The instruments were calibrated to 7993 rpmv methane gas.
1
-------
SECTION 2
RESULTS
This Technical Note presents respond factors for two types of portable
hydrocarbon analyzers, the "OVA-108" and the "TLV sniffer", for 168 differ-
ent chemical compounds. The response factor is defined as the ratio of the
actual concentration to the observed concentration (or instrument response).
The response factor varies with concentration. In a previous report
(Brown, et al^. , 1980) the response factors were presented at 10,000 ppmv
acrual concentration of the chemical.
/
The response factors are computed at 10,000 ppmv concentration observed
by the detector in this Technical Note. Table 2-1 presents response factors
for chamicals on both tvoes of instruments along with the 95 percent confi-
dence intervals. The i ekground Information Document on fugitive emissions
from the Synthetic Organic Chemicals Manufacturing Industry (S0CMI) (EPA,
1980) recommends an action level of 10,000 ppmv as read directly on a por-
table hydrocarbon detector.
Two statistical methods were us;ed here to compute estimates and asso-
ciated confidence intervals: the classical regression method and the inverse
regression method (See Section 3). Both methods of estimation essentially
involve the fitting of a line to the actual and instrument observed concen-
trations. The interpolated or extrapolated actual concentration at 10,000
ppmv observed concentration is calculated based on the fitted line. The
response factor is computed as the ratio of this estimated actual concentra-
tion to the specified 10,000 ppmv "observed" concentration.
-------
TABLE 2-1
RESPONSE FACTORS
WITH M t C0NFI08NCE INTERVALS
ESTIMATED AT 10,000 PPMT RESPONSE
OVA TLV
OCPOB*
COMPOUND
VOLATILITY
RESPONSE
CONFIDENCE
RESPONSE
CONFIDENCE
ID NO
NAME
CLASS*•
FACTOR
INTERVALS
FACTOR
INTERVALS
70
ACETIC ACID
LL
1.64 (
1. 11.
2.65)
18.60
(
7.08 , 46.SO)
•0
ACETIC AfMYDRIDE
LL
1.39 (
I.OB.
1.96)
6.89
I
(
2.71. 12.80)
¦0
ACETONE
LL
0.90 (
0.67.
1.20)
1.22
(
0.81. 2.00)
100
ACETONE CVANOHYDRIN
HL
3.61 (
0.60.
>100.00)
21.00
N
(
1.09.>100.00)
110
ACETONITRILE
LL
0.B5 (
0.S6,
1.06)
1.18
(
0.B4, 1.88)
120
ACETOPHENONE
HL
19.70 (
8.82,
>100.00)
8
S25
ACETYL CHLORIDE
LL
2.04 (
1.72,
2.48)
2.72
(
1.68, 8.18)
130
ACETYLENE
Q
0.39 (
0.36,
0.43)
B
160
ACRYLIC ACID
LL
4.S9 (
3.36.
6.87)
B
170
ACRYLONITRILE
LL
0.B7 (
O.BO,
1.20)
3.48
I
(
0.44, 27.80)
ALLENE
G
0.64 (
0.60,
0.69)
18.00
(
9.88, 26.80)
200
ALLYL ALCOHOL
LL
0.96 (
0.76,
1.27)
X
2SO
ANYL ALCOHOL,H-
HL
0.75 (
0.57,
1.04)
2.14
(
0.48,>100-00)
2155
ANYLENE
LL
0.44 (
0.34,
0.61)
1.03
(
0.89, 2.86)
330
ANISOLE
LL
0.B2 v
0 65.
1.46)
3.91
(
0.82,>100.00)
3BO
BENZALDEHYDE
HL
2.46 (
1.39.
. 8 62)
8
310
. BENZENE
LL
0.28 (
0.2S.
0.31)
1.07
(
0.B6, 1.20)
450
8EN70NITRILE
HL
2.99 (
1 ¦ 18,
18.30)
8
490
BENZOYL CHLORIDE
HL
22.10 D (
3.43,
>100.00)
8
S30
BENZYL CHLORIDE
HL
15.30 D (
3.86,
>100.00)
B
570
BROMOBEK7ENE
LL
0.40 (
0.34,
0.48)
1.19
(
0.27,>100.00)
890
BUTADIENE.i,3-
G
0.87 (
084.
0.60)
10.90
(
8.11, 18.40)
BUTANE.N-
G
0.50 (
0.46,
0.88)
0.83
(
0.88 . 0.70)
B40
BUTANOL.N
LL
1.44 1 (
O.BB,
2.34)
4.11
I
(
2.16, 7.88)
BSC
BUTANOL.SEC-
LL
0.76 (
0.70,
0.93)
1.28
(
0.99. 1.08)
BOO
BUTANOL,TERT
S
0.53 (
0.3B,
0.91)
2. 17
(
1.34, 4.41)
* ORGANIC CHEMICAL PRODUCERS DYTA BASE
«« GsGAS: LL'LIGHT LIQUID; HL-HEAVY LIQUID.
DEFINITION OF EXPLANATORY DATA CODES:
I
0
N
INVERSE ESTIMATION METHOD
POSSIBLE OUTLIERS IN DATA
NARROW RANGE OF DATA
X N9 DATA AVAILABLE
B 10,000 PPNV RESPONSE UNACHIEVABLE
P SUSPECT POINTS ELIMINATED
-------
nri a n t if* n Ti f #**¦ ± • i V
TABLE 2-1 (Continued)
RESPONSE f ACTORS
WITH 88 % CONFIDENCE IHTTBV^t 1
ESTIMATED AT 10,000 PIW RESPONSE
OVA TLV
JCPD0*
COMPOUM)
VOLATILITY
RESPONSE
rimrinrirr
Wliw
RESPONSE
id m
NAME
CLASS**
FACTOR
INTERVALS
FACTOR
INTERVALS
892
BUTEME»1 -
Q
0.50
0-81.
0.B2)
8.84
4.20,
8.88)
BOO
BUTYL ACETATE,
LL
O.BB
0.B4,
0.83)
1 38
1.18,
1.70)
J|M|k
BUTYL ACRYLATE.N-
LL
0.70
0 03.
0 71)
2*87
3
1.17.
tt.tt)
BUTYL ETHER,N
LL
>.00
0.B1,
88.00)
3.88
I
1.82,
7.04)
9UTVL ETHER.SEC
LL
0.3S
0.21,
0.88)
1.18
0 78
2.17)
B70
BUTYLAtflNE.N-
LL
O.BB
0.53,
0.88)
2.02
1-14,'
4.87)
B80
BUTYLAMINE,SEC-
LL
0.70
o.st.
0.87)
1.S8
0.77,
8.24)
BfiO
BUTYI .AMINE, TERT-
LL
0.03
0.88.
0.70)
1.88
1.42,
2.81)
BUTYL8ENZENE,TERT-
HL
1.32
O.BB,
2.20)
B
730
BUTYR ALDEHYDE N-
LL
f.II
1.07,
1.61)
2.30
O.BB,
12.BO)
7B0
BUTYRIC ACID
HL
o.so
0.38.
3.14)
10-70
I
8.S3.
17.80)
780
BUTYRONITRILE
LL
0.82
0. AO,
0.74)
1.47
S
0.B2,
3.48)
790
CARBON DISULFIDE
LL
B
1J2
1.87,
*2.00)
130
CHLOROACETALOEHYDE
LL
t-10
8.73,
1B.20)
8.07
3.08,
• 79)
•90
CHLOROBENZENC
LL
0.38
0.32.
0.47)
0.88
0.77,
1.00)
1740
CHLOROETHANE
€¦
8.38 I
1.87.
28.40)
3.00
P
1.88,
14. IO)
•30
CHLOROFORM
LL
• .21
8.18,
20.00)
B
•80
CHLOROPHENOL.O-
HL
^ * B«
1.72,
27.20)
18.30
2
II Bftr p
81.10)
rui flonllDflDKIAK 4.
LL
0.B7
0.81,
0.73)
O.B?
O.BO.
1.19)
21C
CHLOROPROPENE, 3-
LL
O.SO
0.72,
O.SO)
1.24
1.08,
1.42)
•70
CHLOROTQLUENE.M-
LL
0.48
0.48.
0.91)
0.91
0.40,
7.47)
NO
CHLOROTOLUENE,0-
LL
0.41
0.42,
0.88)
1 .OB
0.33.>100.00)
99C
CHLOROTOLUENE.P-
LL
0.86
0.82,
0.B1)
1, |7
I
0.77,
1.77)
IC'fS
CRESOL,0-
S
0.96
0.70.
1.48)
# «dPD
1
0.40,
47.40)
1040
CROTONALDEHYDE
LL
1.2S
0.82,
2.24)
B
• ORGANIC CHEMICAL PRODUCERS DATA. BASE
»» G=CAS; LL-LIGHT LIQUID; HL'HEAVY LIQUID.
DEFINITION OF EXPLANATORY DATA COOES:
I INVERSE ESTIMATION METHOD X NO DATA AVAILABLE
D POSSIBLE OUTLIERS IN OATA B 10.000 PPNV RESPONSE UNACHIEVABLE
N Nj WHOM RANK OF OATA P SUSPECT POINTS ELIMINATED
-------
TAELE 2-1 (Continued)
RESPONSE FACTORS
WITH BB * G0NF1BBNC
ESTIMATES AT 10,000
1 INTERVALS
PPW RESPONSE
OVA
TLV
DCPOB*
COMPOUND
VOLATILITY
RESPONSE
CONFIDENCE
RESPONSE
CONFIDENCE
ID NO
MJUK
CLASS**
FACTOR
INTERVALS
FACTOR
INTERVALS
1080
CUMENE
LL
1.87
1.10
3.71)
8
1120
CYCLOHEXANE
LL
0.47
0.38
0.88)
0,70
C 0.82, 0.80)
1130
CYCLOHEXANOL
HL
o.ss
0.88
1.20)
B
1140
CYCLOHFXANGNE
LL
1.80
0.87
2.78)
7.04
( 1.88, >100.001
11BO
CYCLOHEXENE
LL
048
0.42
0.87)
2.17
( 1.78, 2.74)
11SO
nyevvi fMTilff
yi ViWHAI
LL
0.57
0.42
0.88)
1.38
( 1.28, 1.48)
DECANE
HL
0.08 N
0.08
>100.00)
0.18
I
( 0.07, 0.38)
1190
DI ACETONE ALCOHOL
HL
1.48
0.81
2 48)
0.88
{ 0.44, B.B3)
DIACETYL
LL
1.S4
1.28
1.82)
3.28
( 2.28, 8.13)
1270
OICHLORO-1-PROPENE,2.3-
LL
0.71
0.18
1.08)
1.78
< 1.14, 3,18)
1215
fMtvjngji Rg__
If*
HL
0.04
0.88
0.77)
2.38
( 0,88,>100.00)
1216
OICHLOROSENZENC.0-
vrL
0.80
0.47
1.11)
1.28
( 0.38,>100.00)
DICHLOROETHANE,1,1-
LL
0.78
0.82
1.02)
1.88
( 1.58, 2.28)
«244
m.tm MAfWWJ J|*jW 4 0% _
DI i p * § 3»
LL
0 * 88
0.77
1.22)
2.18
( 1.08, 2.82)
1235
DI CHLOROETHYLENE. CIS 1.2-
LL
1 27
1.08
1.98)
1.83
( 0.88, 3.47)
1238
D1CHLOROETHYLENE. TRANS 1.
2 LL
flit
0.88
127)
1.88
{ 0.87, 12.80)
2820
DICHLQROMETHANE
LL
2.81
m # 1#
3.87)
w • 09
i ) ia « in
^ w « § iNr • wW j
3110
OICMLOROPROPANE,1,2-
LL
1. 03
0.82
1.33)
1.88
( 1.08, 3.08)
1440
01ISOBUTYLENE
LL
0.3S
0.28
0.44)
1.41
< 0.88, 2.40)
1S70
OlMETHOXY ETHANE,1,2-
LL
1.22
0.84
1.81)
1.B2
< 0.88, 8.38)
14*0
OIMETHYLFORMAMIDE.N.N-
LL
4. IB
2.80
8.88)
8.28
( 4.OS, 7.20)
1485
DIMETHYLHYDRAZINE 1,1-
LL
1.03
0.77
1.48)
2.70
( 0.81,>100.00)
1B20
DIMETHYLSULFOXIDE
HL '
0.07 I
0.08
0.11)
8.48
I
( 4.18, 17.20)
14«0
DIOXAME
LL
1.48
1.04
2.33)
1.31
( 0.70, 3.80)
1090
PftVMi JHUHMMtt.
fc™ AvVnwUjNSLnrl ¦ URJIW
LL
*.88
f .88
1.84)
2.03
( 1.*7B! 2.3*)
• ORGANIC CHEMICAL PRODUCERS DATA RASE
m G'GAS; LL*LIGHT LIQUID; HL'HEAW LIQUID.
DEFINITION Of EXPLANATORY DATA COOES:
I
D
M
INVERSE ESTIMATION METHOD X ND DATA AVAILABLE
POSSIBLE OUTLIERS IM DATA B 10,000 PPHV RESPONSE UNACHIEVABLE
NARROW RAN6E OF DATA P SUSPECT POINTS ELIMINATED
-------
TABLE 2-1 (Continued)
bijfont factors
MTH * amwam intervals
ESTIMATED AT 10,000 PPMV RESPONSE
OVA
TLV
DCPOB*
COMPOUND
VOLATILITY
RESPONSE
CONFIDENCE
RESPONSE
CONFIDENCE
ID NO
MftMC
FACTOR
INTERVALS
INTERVALS
ETHANE
0
0.05
( 0.44.
1.88)
0.09
I
(
0.21, 2.80)
rxQ
ETHANOL
LL
1.78
( 1.89,
2.01)
X
1810
ETHOXY ETHANOL,2-
LL
1.55
( f .28,
1.98)
1.82
(
0.88, 8.18)
1870
ETHYL ACETATE
LL
0.88
< 0.77,
0.98)
1.43
{
1.07, 2.00)
1880
ETHYL ACETOACETATE
HL
3.92
( 1.89.
10.70)
8.80
C
1.93. 38.80)
1S90
ETHYL ACRYLATE
LL
0.77
f 0.03,
0.97)
X
17SO
ETHYL CHLOROACETATE
LL
1.99
< 1.70,
2.38)
*.19
f
0.40,>100.00)
1990
ETHYL ETHER
LL
0.97
C 0.77,
1.30)
1,14
c
0.94, 1.48)
1710
ETHYL9INZENE
LL
0.73
( 0.82,
1.11)
4.74
0
(
1.38, 81.30)
1170
ETHYLENE
Q
0.71
( 0.83.
0.82)
1.98
c
1 28 2 OS)
1980
ETHYLENE OXIDE
0
2.40
< 1.98.
3.29)
2 40
c
0.'98.'»100!00)
1B00
ETHYLENEDI AMINE
LL
1.73
( 1.29.
2.48)
3.28
c
0.78,>1001.00)
2080
FORMIC ACID
LL
14 20
( 10.80.
19.80)
B
210S
OLYCIDOL
LL
8.88
( 3.33.
19.70)
8.88
<
2.08, 34.70)
MPDTWE
LL
0.41 I
C 8.28,
0.80)
0.73
<
0.33, 8.10)
LL
0.41
( 0.38.
0.48)
0.89
c
0.83. 0.78)
HEXENE,1-
LL
0.49
C 0.39.
0.88)
4.89
D
c
0.88.>100-00)
HYDROXYACETONE
LL
0.90
( 4.48.
12.10)
18.20
<
8.11. 88.40)
ISOBUTANE
a
0.41
^ 0 # 29,
1.04)
0.85
(
0.41. 0.81)
9200
IdOBIfTYLENE
0
3.13
( 0.90.
38.80)
8
2350
LL
0.59
< 0.48,
0.80)
X
.
2980
ISOPROPANOL
LL
0.91
C 0.72,
1.20)
1.39
f
0.94, 2.91)
2370
ISOPROPYL ACETATE
LL
0.71
( 0.82,
0.93)
1.31
<
1.04. 1.72)
2390
ISOPROPYL CHLORIDE
LL
0.98
( 0.80.
0.77)
0.98
(
0.82, 1.22)
ISOVALERALDEHYDE
LL
0.64
( 0.57,
0.74)
2.19
D
<
1.14, 8.88)
• ORGANIC CHEMICAL PRODUCERS DATA BASE
*~ G-GAS; LL-LlOfT LIQUID; HL-HEAVY LIQUID.
DEFINITION Of EXPLANATORY DATA COOES;
I INVERSE ESTIMATION METHOD X NO DATA AVAILABLE
D POSSIBLE OUTLIERS KM DATA « 10,000 PPMIf RCSPOMSf UNACHIEVABLE
N NARROW RAN8E OF DATA P SUSPECT POINTS ELIMINATED
-------
TABLE 2-1 (Continued)
IftHI M % CONFIDENCEINTERVALS
ESflMATCD AT 10.000 PfMV RESPONSE
OVA TLV
dcpob*
COMPOUND
VOLATILITY
RESPONSE
CONFIDENCE
¦rifWKF
CONFIDENCE
ID NO
NAME
CLASS**
FACTOR
INTERVALS
m a
w
INTERVALS
2450
MESITYL OXIDE
LL
1.00
0.94.
1.291
3.14
1.43.
12.00)
NETHACROLEIN
LL
1.20
0.90.
1.71J
3.49
D (
1.81.
19.90)
3480
METHACRYLIC ACID
HL
0.82
0.31,
14.70)
1.08
Z (
0.24.
4.B8)
2500
METHANOL
LL
4.39 P
3Jfi
5.80)
2.01
1».
2.48)
1930
METHOXY -ETHANOl. 2-
LL
2,25
1.82,
3.34)
3*13
1.13.
27.40)
2810
METHYL ACETATE
LL
1.74
1.48,
2.13)
1.98
1.44,
2.49)
METHVL ACETYLENE
6
0.81
0.88,
0.84)
8.79
4.88,
10.40)
2560
METHYL CHLORIDE
G
1.44
1.22,
1.78)
1.94
0.73.>100.00)
3840
METHYL ETHYL KETONE
LL
0.84
0.B1,
0.84)
1.12
0.83,
1.38)
2^J45
METHYL FORMATE
LL
3.11
2.42
4.14)
1.94
1.72.
2.21$
2065
METHYL METHACRYLATE
LL
0.99
0.90,
1.10)
2.42
1. ,
8.38)
NETHYL-2-PENTAN0L, 4-
LL
1.88
1.27.
2.32)
2.00
140.
3.18)
2800
METHYL-2-PENTANRNE. 4-
LL
0.98
0.48.
0.89)
1.03
1.22.
2.38)
2B5G
METHYL-3-B»JTY!f-?-0L, 2
LL
0 • 5fT
0.44,
O.B8)
X
METHYLAL
LL
1.37
1.08,
¦ 1.83)
1.48
1.24,
1.78)
2540
METHYLAWILIME.N-
HL
4.84
3.91.
8.87)
9.46
I (
2.65,
38.20)
2570
METHYLCYCLOHEXANE
LL
0.48
0.28.
1.39)
0.84
1.08)
METHYLCYCLOHEXENE, 1-
LL
0.44
0.38.
0.54)
2.79
* .79.
8.12)
2070
METHYLPENTYNOL
LL.
1.17
0.71,
2.49)
3.42
1.93,
8.84)
2890
METHYLSTYRENE, A-
LL
13.90
9.BO,
21.SO)
B
2700
MORPHOLINE
LL
0.92
0.87,
1.40)
2.59
X <
0.84,
10.80)
1770
NX TROBErlZENE
HL
B
O.Ol
I (
0.00,
92.80)
2790
NITffOETHANE
1.40
1.20,
185)
3.45
1.88,
13.00)
2791
NITRONETHANE
LL
3.52
3.03,
4.15)
7.80
1.91, >100.00)
2795
HI
LL
1.0S
0.90,
t. 49 )
2.02
1.17,
4.47)
* ORGANIC CHEMICAL PRODUCERS DATA BASE
*• G*GAS; LL'LHSfT I.IQUIO; ML'WAVY LIQUID.
DEFINITION OF EXPLANATORY DATA GOOES:
I INVERSE ESTIMATION METHOD X NO DATA AVAILABLE
O POSSIBLE OUTLIERS IN DATA B 10,000 PPNV RESPONSE UNACHIEVABLE
N NARROW RAN8E OF 0#TA P SUSPECT POINTS ELIMINATED
-------
TABLE 2-1 (Contimi-d)
Msxwst "r*ims" —
with w * oawioaacc intervals
ESTIMATED AT 10.000 PPMV RESPONSE
OVA I TLV
ocpdu*
COMPOUND VOLATILITY RESPONSE
CONFIDENCE
RESP#C
IE
CONFIDENCE
ID ND
NAME
CLASS** FACTOR
INTERVALS
FACTtN
INTERVALS
NONANE-N
LL
1.54 (
0.94
2.99)
11.10
3.13 .>100.00)
OCTANE
LL
1.03 (
0.99
1.21)
2. ll
1.89.
2.79)
2§S1
PfffTANE
LL
0.92 (
0.42
0.99)
0.83
0.97,
0.70)
2973
PIC0L1ME,2-
'A
0.43 (
0.39
0.90)
1.19
1.09,
t.29)
PROPANE
a
0.99 I (
0.40
0.72)
0.00
P (
0.99,
0.89)
3003
PROPIONALDEHVOE
LL
1.14 (
1.00
1.32)
1.71
\ C
1.11,
9.08)
¦M*
PROPIONIC ACID
LL
1.30 (
1.03
1.70)
9.09
0 t
0.73 ,>100.00)
3070
PROPYL ALCOHOL
LL
0.93 <
0.77
1.19)
1.74
1.09,
3.90)
PROPYLfiENZENE.N-
LL
0.91 (
0.49
0.99)
1 1
9090
PROPYLENE
G
0.77 C
0.44
2.90)
1.74
I (
0.19.
20.10)
m l4v
PROPYLENE OXIDE
LL
0.93 i
0.74
0.99)
1.13
0.99,
2.48)
3130
pyridine
LL
0.47 <
0.40
0.99)
1.19
1.03.
1.34)
9230
STYRENE
LL
4.22 (
3.49
9.27)
9
3290
TETRAGHLOROETHANE. 1,1»1 f 2
LL
4.93 D C
1.24
>100.00)
9.91
3.14,
22.80)
|39f
TET5m^i.0R0ETHAME .1.1,2.2
LL
7.99 (
9.01
. 13.SO)
29.40
9.09. >100.00)
3690
TETRACHLOROETHYLENE
LL
2.97 (
1.71
9.11)
9
3349
TOLUENE
LL
0.39 (
0.39
0.43}
2.99
D (
0.79. >100.00)
3383
TRICMLOROBEHZEHE,1.2.4-
HL
1.21 I {
0.90
2.94)
0.47
I <
0.32,
0.89)
3395
TRICHLOROETHANE. 1. 4 ,1-
LL
0.80 (
0.72
0.90)
2.40
1.91,
3.38)
3400
TRICHLOR0CTHANE, 1,1.2-
LL
1.29 (
1.09
1.90)
3 99
2.77,
9.18)
3440
TRICHLOROiTHYLENE
LL
0.9S (
0.93
1.09)
3.83
2.89,
8.92)
3430
TRICMLOROPROPANE.1.2.3-
LL
0.9S (
0.94
1.79)
1.99
1.27,
9.92)
3450
TRS ETHYLAMINE
LL
0.91 (
0.40
0.70)
1.49
0.98.
2.78)
3910
VINYL ACETATE
LL
1.27 (
0.99
1.92)
9.91
0 (
1.28. >100.00)
3920
VIMVL CHLORIDE
G
0.94 (
0.91
1.39)
1.09
0.99,
4.80)
*
ORGANIC CHEMICAL PRODUCERS
DATA BASE
** G«OAS; LL«LIGHT LIQUID; HL'HtAVfY
LIQUID.
DEFINITION OF EXPLANATORY DATA CODES:
1
INVERSE ESTIMATION METHOD
X
ND DATA AVAILABLE
0
POSSIBLE OUTLIERS IN DATA
B
10,000 PPMV RE!
IPONSE
UNACHIEVABLE
N
NARROW RANOE OF DATA
P
SUSPECT POINTS
ELIMINATED
-------
TABLE 2-1 (Continued)
RESPONSE FACTIMS
WITH M % CONFIOMQK INTERVALS
ESTIMATED AT 10,300 WW RESPONSE
OVA
TLV
OCPOB*
ID ND
myn»iui|
NAME
VOLATILITY RESPONSE
CLASS*» FACTOR
CONFIDENCE
INTERVALS
RESPONSE
FACTOR
CONFIDENCE
INTERVALS
VINYL PROPIONATE
LL
1.00 I (
0.«7,
1.74)
1.31
I
(
0.40, 3.30)
3830
VINYLIDENE CHLORIDE
LL
1.12 (
0*7,
1 -82)
2.41
C
1 At 9 9RI
V m V » g fr
3970
mwi *k
in V laSHrHEL |
Li.
2.12 (
1.t1,
2.OS)
7.S7
«
3.49, 24.M)
3550
XYLENE, M-
0.40 (
0-30,
0 46)
S.17
D
C
0.11, >100.00)
jam
XYLENE.O-
LL
0.43 C
0.2S,
O.SS)
1.40
<
0.01, 0.99)
* ORGANIC CHEMICAL PRODUCERS rJATA DASE
»* G-GAS; LL-LIGHT LIQUID; ML'HEAVY LIQUID.
DEFINITION OF -EXPLANATORY DATA CODES:
V INVERSE ESTIMATION NETMD& X M> DATA AVAILMU
0 POSSIBLE OUTLIERS IN DATA ¦ '<0.000 PPMV RESPONSE UNACHIEVABLE
N NARROW RANGE OF DATA P SUSPECT POINTS ELIMINATED
-------
Most of the response factors and associated confidence intervals were
calculated using the classical method; those computed using the Inverse
method are noted in Table 2-1 with the explanatory code "I". Other explan-
atory codes used in Table 2-1 indicate data availability, data applicability
and possible data uncertainties such as the presence of outliers.
In most cases the data fell very nearly on a straight line, but some-
times th«y Jid not. When outliers were clearly defined they were removed
from the data and the response factor recomputed. This could not always be
done. Often it was not clear which data points were valid and which were
not. Additional data would be necessary to clarify these situations. Since
it was not clear whicn points should be removed in these cases, all points
were included.
Table 2-2 lists chemicals tested which do not appear to respond at a
10,000 ppmv reading at any concentration. The data and the fitted line
showed that the response appears to be well below 10,000 ppmv for feasible
actual concentrations. Sometimes it was not possible to distinguish between
this situation and the problem of unresolved outliers mentioned above. Ques
tionable or borderline cases are included in Table 2-1 rather than Table 2-2
Some of these chemicals have large estimated response factors and wide con-
fidence intervals.
10
-------
TABLE 2-2.
A LIST OF TESTED CHEMICALS WHICH APPEAR TO BE UNABLE TO
ACHIEVE AN INSTRUMENT RESPONSE OF 10,000 PPMV AT ANY
FEASIBLE CONCENTRATION
OCPDB*
OVA
Compound Name
OCPDB
TLV
Compound Name
790
810
1221
2073
1660
2770
2910
Acetyl-l-propanol, 3-
Carbon disulfide
Carbon tetrachloride
Dichloro-l-propanol,2,3-
Dichloro-2-propanol,1,3-
Diisopropyl benzene,1,3-
Dimethylstyrene,2,4
Freon 12
Furfural
Methyl-2,4-Pentanediol,2-
Monoethanolamine
Nitrobenzene
Phenol
Phenyl-2-Propanol,2-
120
130
160
360
450
490
530
810
930
1040
1060
1130
2060
1221
2073
2200
2690
1660
2910
3230
2860
Acetophenone
Acetyl-l-propanol, 3-
Acetylene
Acrylic Acid
Benzaldehyde
Benzonitrile
Benzoyl chloride
Benzyl chloride
Butylbenzene, tert-
Carbon tetrachloride
Chloroform
Crotonaldehyde
Cumene
Cyclohexanol
Dichloro-l-propanol, 2,3-
Dichloro-2-propanol,1,3-
Diisopropyl benzene,1,3-
Dimethylstyrene,2,4-
Formic acid
Freon 12
Furfural
Isobutylene
Methyl-2,4-pentanediol
Methylstyrene, A-
Monoethanolamine
Phenol
Phenyl-2-propanol,2-
Propylbenzene,N-
Styrene
Tetrachloroethylene
*0rganic Chemiral Producers Data Base ID Number
11
-------
SECTION 3
DATA ANALYSIS
The estimated response factors at 10,000 ppmv for the OVA and TLV were
calculated as follows: A classical least squares line van fitted to the
actual concentrations and instrument response readings or logarithmic scale.
The logarithm of the actual concentration at response log 10,000 was then com-
puted by solving the equation using the fitted parameters. The result was
I
then transformed to the data scale and divided by 10,000 to yield the desired
response factor, A 95 percent confidence interval was computed following
Brovmlee (1965). Ihe results are presented in Table 2-1.
In some cases Brownlee's (1965) confidence interval gives indeterminate
values. This generally is due to a regression line that is flat relative to
the observed error or to other data problems. Response factors estimated by
an inverse regression were generally agreeable to the method described above.
In those cases where the confidence interval was indeterminate, the inverse
regression estimate and confidence interval were computed as an alternate.
These inverse estimates are indicated in Table 2-1 by an explanatory code "I".
3o1 Classical Estimation of Response Factors
Let c^ be the actual concentration cf the selected chemical and r^ be
the corresponding instrument response for i - 1,..., n observations. Con-
sider then the transformed v&riates
yt " ln ri
x, ¦ ln c.
i i
12
-------
and Che relationship
y1 = ex + £xt +¦
(1)
where is a random error of measurement. Let a and b be Che classical
lease squares estimates of a and |3, respectively.
Now, suppose that at some unknown x
In 10,000 - a + 6*
Then estimate x by
o J
x ¦ (In 10,000 - a)/b
Ol
and estimate the actual concentration corresponding to 10,000 ppmv observed
instrument response by
c = exp(x ).
Ol O!
A confidence interval base(' on classical least squares estimation
derived by Brownlee. (19fi5):
CL, = x +
bll ~ a)
Ck8
b2 - t£s2/ ^(Xi - x)2 b2 - t2s2/ X)(xL - X)-
t?B
b2 - k
J>.i -
(+) *
( - a)
13
-------
where k « 1,2
11 - +t and 12 ¦ -t, with t being the tabular value for 95 percent
confidence from student's t-distribution with n-2 degrees of
f reedom,
s2 ¦ 5!;(y^ ~ 9^) (n-2), with y^ = a + bx^, and
» In 10»0'J0 (In Brownlee, this is the mean of m observed
resporses, Here, the desired response is exact, so
m - and 1/m ¦ 0).
The value CLz provides the lower limit and CLi provides the upper limit.
These limits were computed in the logarithmic scale and then exponentiated
into the data scale.
3.2 Inverse Estimation of Response Factors
Let x^ and y^ be as described abo\e except that the inverse model
relationship
- 6 + yy± + ^ (2)
is fitted by least squares. Let d and g be the estimates of 6 and y«
respectively. Then if
x * 6 + Y'ln 10,000
o
estimate x by
o J
X * d + g«l» 10,000.
o2
14
-------
Assuming normality of the errors ,
s2
c = exp(x + J ) (3)
~ 2 ~i2
is an approximately unbiased estimate of
c « exp(x )
o ' o
>5
where s is the estimated variance of the c^.
A confidence interval for * can be computed bv the usual method;
o
x + ts /- + (x - x)3/I(x, - x)2
oz y n o l
where t is the 95 percent confidence level tabular value from Student s
t-distribution with n-2 decrees of freedom. The confidence limits for c
o2
are computed by applying the transformation of (3) to theue limits for x^.
3,3 Discussion
Both of the models (1") and (?) cannot be correct simultaneously. If
the model (2) is correct for the data, then the second cr inverse approach
is appropriate. However, if tha model (1) is correct, '.hen both approaches
produce biased estim:ics. Ce.nc.ral ly speaking, the bia* of the classical
method will be smaller since it is a consistent estimator (bias reduces to
zero as sample size increases without bound). The variance, however, mt.y
tend to be largsr.
The model (1) jppeaes to best approximate the d.tt i collected for this
study. The classical approach was used as the primary method in this report
15
-------
because of its consistency and reputed superiority in extrapolation. The
properties of the data for most of the chemicals are ^uch that the two
approaches are virtually equivalent. A comparison of computed values con-
firmed this hypothesis.
16
-------
-------
SECTION 4
LITERATURE REVIEW
The statistical literature is clear on how to estimate y for a given x
when y and x are related by
y - a + 0x
and y is subject to error. There has been much disagreement on how to
estimate an unknown x given on observed value cJ y in the same situation.
For many years it was universally assumed that ;:he unknown x should be
solved for using the usual parameter estimates. Some have suggested that
the parameters be fitted by an inverse "x on y" regression and the unknown
x estimated directly. There has been consirferabla controversy over this
an-i some classic assumptions have proven unfounded.
The properties of the two estimates -ire summarized in the following
table:
Classic Inverse
Property (y on x) (x on y)
Bias
Assymptotic Bias
Variance
—Under Normality
—Truncated Normality
Quality as Estimator
—We11 determined line
—Interpolation with ill
determined line
—Extrapolation
Riasea
Consistent
Infinite
Large but Flni'.e
Biased
Inconsistent
Finite
Finite
Both good and equivalent
Poor
Good
Good
Poor
11
-------
In this study, many of the needed estimates are extrapolations just beyond
the end of the available data. Many of the lines are fairly well determined.
Thus, it is not completely clear which estimate is truly best here, but they
are likely to be nearJy equivalent. For this study, the classic estimator
is used except in cases where it is clearly not appropriate. The inverse
estimator is used for the?e cases.
The following is a summary of the literature examined on this subject:
The relationship between tw j variables y and x can often be expressed
as a simple linear function. If the variable x takes on fixed values
for which responses yi are measured, the relationship is usually expressed
as the linear regression model
y, = a + (3x, + e, i = 1, . . , ,n (1)
1 l i
where the e^ are random errors and n is the number of observed pairs
(x^, y^). It is usually assumed that the are independent and identically
distributed, and furthermore, that they are distributed according to a
normal distribution with mean 0 and variance o2,
It is well known that the usual least squares estimates of a and 8
in (1) are Best Linear Unbiased Estimators (BLUE), where "Best" means
"smallest variance". Estimates of y, = a + £x based on the least squares
estimates of a and B are also BLUE, Under the assumption of normality of
errors, these estimates are also maximum likelihood estimates. The least
squares estimators have many other useful and beneficial properties.
Here we must consider a slightly different problem known as the
Calibration Problem. In addition to the responses y,^ on known ju, there
are further responses corresponding to an unknown Xq. The extended
18
-------
I
model is
yt - a + Bxi + i = (2)
z. - a + 3xq + ©j j = (3)
The problem here is to provide point and interval estimates for xq rather
than to estimate y. ,a , or 6.
1.
The above discussion closely follows Kalotay (1971).
At least since Eisenhart (1939) the accepted solution has been to
estimate the unknown x by inverting the least squares estimates from (2):
o
where z is the mean of the in (3) and a and b are the least squares
estimates of a and 3 respectively. This is referred to as the "classical"
estimator,
Krutchkoff (1967, 1969) challenged this approach by claiming that a
superior estimate could be had by inverting the regression variables; that
is, compute the least squares estimates of o and y from the model
x. = 6+ yy.+£,
± J i i
and estimating the unknown xq directly by
x = d + g z
oz
where d and g are the least, squares estimates of 5 and y respectively.
19
-------
This is referred to as the "inverse" estimator, Krutdkof f based his
assertion not on mathematical statistical properties but on Monte Carlo
simulations.
4fter Krutchkoff's results appeared there was a flurry of reaction.
Williams (1969) reported t.iat if normality of errors was assumeds then the
classical estimator x has infinite variance. He showed further that no
Oj
unbiased estimate of x would have finite variance under this condition and
o
that the inverse estimator x is biased. On this basis he recommends the
o2
classical estimator.
Berkson (1969) showed that the inverse estimator x has a smaller
0 2
Mean Square Error (MSE) than the classical estimator :l when x is in the
_ Oi o
neighborhood of x, the mean of the x.'s. However, if x is not near x then
i o
the classical estimator V as lower MSE. Furthermore, the inverse estimator
is not only biased for finite n bu is inconsistent: Hie bias does not
reduce to zero as n increases without bound. On this basis he also recom-
mends the classical estimator. Martinelle (1970), looking at relative
efficiency, agrees with Berkson. Saw (1970) agw;s with Martinelle on the
same basis.
Hoadly (1970) reaffirms that the classical estimator has infinite
variance if normality is assumed. It may also have infinite confidence
intervals. He then proposes an alternative solution based on Bayesian
methods,
Williams (1969) had suggested that an MaE comparison was inappropriate
since under normality the classical estimator always has infinite MSE so any
finite MiJE estimate could beat it, including any constant value. To avoid
this Halperin (1970) compares the two approaches based on Pitman's ~losenest
criterion. He showed that the inverse estimator was stipeiior in the
neighborhood of x. However, he believes that the neighborhood where the
inverse estimator is superior is too small to recommend it over the
20
-------
classical estimator.
%
\
Krutehkoff (1970, 1971, .1972) defended his point of view primarily
with Monte Carlo simulations. His results indicatesthat the inverse
estimator is better by the closeness criterion when x s near x. The
V.
classical estimator is better further out from x. v '•*
Kalotay (1971), recognizing that the classical estimator has certain
v
unsatisfactory properties', proposes an alternative estimator which he ^
%
compares to Hoadley's (1970) Bayesian estimator. Kalotay's structural ^
solution to the problem is not practical for any but very small sample
sizes. He points out that under certain conditions his estimator reduces to
the inverse estimator.
Shukla (1972) developed approximate formulas for bias, variance, and
MSE of both classical and inverse estimators. He shows that both are
biased but that the classical estimator is assymptotically unbiased, unlike
the inverse estimator. However, both biases reduce to zero when the unknown
xq is at the mean of the Using the optimal design for the classical
estimator, the inverse estimator has smaller H5E than the classical estima-
tor in the range of the Nevertheless, Shukla (1972) recommends the
classical estimator for its bias properties.
Earlier critics of the Inverse"estimator rejected it because it is not
only biased but inconsistent. The classical estimates for a, 8, and y are
unbiased but it was not proven that the classical estimator x is unbiased
°i
for x , Naszodi (1978) shows that the classical estimator is also biased.
o
Furthermore, if normality is assumed, it has no expectation.
Naszodi (1978) points out that in practical problems, perfect normality
rarely exists. In fact, even when data errors are normal, extreme values
will generally be discarded. Tims, in reality the distribution is a
truncated normal. In any case, Naszodi (1978) gives a new estimator •,
21
-------
involving an approximate bias correction for the classical estimator.
Based on a simulation, all three estimators appear to have about the same
MSE with the inverse estimator having the lowest, and the classical the
highest.
Brown (1979) points out that the objectives of the estimation in (1)
and in the calibration problem (2) and (3) are different. There is no
argument that the classical approach is "best" for estimating a and 3. In
the calibration problem, the objective is the estimation of the unknown x^.
Brown's (19"9) initial approach is to find the minimum MSE linear
estimator of x . He shows, however, that the MSE of a linear estimator
c
depends on x^. To cope with this he proposes an unspecified distribution
of futu e XQ'S to be estimated. After integrating the MSE over this distri-
bution, a wjw minimjm integrated MSE estimator (1MSE) is obtained.
flrovn C1979^ does not propose his minimum IMS£ estimator for general
use, &1'.hough ha notes that it could be used in some cases. He uses it as
vvs a benchmark tr compare the classical and inverse estimators. When the
repress:.on line is well de:ermined by the data, the two etstimators are
virtually equivalent. When the regression line is ill determined, the
classic;. ] ostimator is vtM^ bad. The inversa estimator will be very good
it the jean of the calibriition-vjample x is near the expected value of the
*V"~.
future unknown x 's. If :he range nf future: x 's is large relative to the
o x - o
range oi the calibration x^'s, then the inverse estimator is very bad while
the classical estimator is very good.
The previous discussion applies to poi.it estimates. Much less is
said about interval estimates for confidence intervals. Williams (1969)
suggests that the two point estimators should be compared on the basis of
confidence intervals. Shulka (1972), referring to this, states that it is
not clear how a confidence interval can be constructed for the classical
estimate. The usual method of estimating a confidence interval for a
22
-------
predicted response may be applied in reverse to give a confidence interval
for the inverse estimator.
Brovmlee (1965) gives a confidence internal based on the classical
estimation method, Naszodi (1978) refers to this interval without comment.
Hoadley (1970) comments that a confidence interval for the classical
estimator may be infinite. Trout and Swallow (1971) describe Scheffe
confidence bounds for individual observations. They then derive uniform
confidence ban is over a specified range of x.
23
-------
REFERENCES
Berkson, J. (1969), Estimation of a Linear Function for a Calibration Line:
Consideration of a Recent Proposal. Technometrics, 21, 649,
Brown, G, E., D. A. DuBose, W. R. Phillips, and G. E. Harris, "Response
Factors of VOC Analyzers Calibrated with Methane for Selected Organic
Chemicals", EPA Report Ho. 600/2-81-002 (NTIS NO. PE81-136194) ,
Research Triangle Park, N.C., 1980,
Brown, I. H. (1979), An Optimization Criterion for Linear Inverse Estimation,
Technometrics, 21, 575.
Brownlee, K. k. (1965). Statistical Theory and Methodology in Science and
Engineerings, New York: John Wiley & Sons, Inc.
Eisenhart, C, (1939). The Interpretation of Certain Regression Methods and
Their Use in Biological and Industrial Research. Annals of Mathematical
Statistics, 10, 162.
Environmental Protection Agency, VOC Fugitive Emissions in Synthetic Organic
Chemicals Manufacturing Industry—Background Information for Proposed
Standards, Emission Standards and Engineering Division, Research Triangle
Park, N.C., March, 1980 (Draft).
Haljerin, M. (1970). On Inverse Estimation in Linear Regression, Technometrics,
12, 727.
Hoadley, B. (1970). A Bayesian look at Inverse Linear Regression. J. Amer.
Statist. Assoc., 65, 356.
Kalotay, A. J. (1971). Structural Solution to the Linear Calibration Problem.
Technometrics, 13, 761.
Krutchkoff, R, G. (1967). Classical and Inva-se Regression Methods of Cali-
bration. Technometrics, 9_, '?5.
Krutchkoff, R. G. (1968). Letter to Editor. Technometrics, 10, 430.
Krutchkoff, R. G. (1969). Classical and Inverse Regression Methods of Cali-
bration in Extrapolation. Technometrics, 11, 605,
Krutchkoff, R. G. (1970). Letter to Editor. Technometrics, 12, 433.
Krutchkoff, R. G. (1971). The Calibration Problem and Closeness. Journal
of Statistical Computation and Simulation I, 87.
Krutchkoff, R. G. (1972). Letter to Editor. Technometrics, 14, 241.
24
-------
Martinelle, S. (1970). On the Choice of Regression of Linear Calibration.
Comments on a paper by R. G. Krutchkoff. Technometrica, 12, 157.
Naszodi, L. J. (1978). Elimination of the Bias in the Course of Calibration.
Technometrics, 20, 201.
Saw, J. G. (1970). Letter to Editor. Technomc'rlcs, 12, 937.
Shuckla, G. K. (1972). On the Problem of Calibration. Technometrics, 14,
547.
Trout, J. R. and W. H. Swallow (1979). Regular and Inverse Interval Esti-
mation of Individual Observations Using Uniform Confidence Band J.
Technometrics, 2.1, 567 .
Williams, E. J. (1969). A Note on Regression Methods in Calibration.
Technometrics, 11, 189.
25
-------
TECHNICAL REPORT DATA
(PkMt trad Imttmchons on the rtvtru btfort computing)
i. report no. j.
EPA-600/2-81-051
3. RECIPIENT'S ACCESSION NO.
MM 7
4. TITLE ANO SUBTITLE
Response Factors of VOC Analyzers at a Meter
Reading of 10,000 ppmv for Selected Organic
Compounds
S. REPORT DATE
March 1981
S. PERFORMING ORGANIZ'.TION c:od«
7. AUTMOR(S)
D. A. DuBose and G. E. Harris
1,. PERFORMING ORGANIZATION REPORT NO.
B. PERFORMING OAOANIZATlON NAME ANO ADDRESS
Radian Corporation
P.O. Box 9948
Austin, Texas 78766
10. PROGRAM ElFMENT NO.
1AB604
11. CONTRACt/GRANT NO.
68-02-3171, Task 28
12. SPONSORING AGENCY NAME AND AOORESS
EPA, Office of Research and Development
Industrial Environmental Research Laboratory
Research Triangle Park, NC 27711
13. TYPE OP REPORT AND PERIOD COVERED
Task Final: 12/80-2/81
14. SPONSORING AGENCY CODE
EPA/600/13
is. supplementary notes ierl-RTP project officer is Bruce A. Tichenor, Mail Drop 62,
919/541-2547. EPA-600/2-81-002 is a related report.
is. abstract report summarizes results of a relnterpretation of data generated In
a laboratory study of the sensitivity of two types of portable hydrocarbon detectors
to a variety of organic chemicals. (A previous report, EPA-600/2-81-002, des-
cribes and gives original results of the laboratory study.) Detector sensitivity is
quantified by a response factor for each chemical where the response factor equals
the actual concentration of the chemical divided by the observed concentration from
the detector. The previous report estimated response factors at 10,000 ppmv actual
concentration of the chemical. This report presents response factors estimated for
a 10,000 ppmv detector reading. The instruments were calibrated to 7933 ppmv
methane gas.
17. KEV WORDS AND DOCUMENT ANALYSIS
1. DESCRIPTORS
b.IDENTIFIERS/OPEN ENDEO TfeRMS
c. cosati Field/Croup
Pollution
Hydrocarbons
Measuring Instruments
Sensitivity
Organic Compounds
Pollution Contiol
Stationary Sources
Hydrocarbon Detectors
Response Factors
13 B
07 C
14B
14G
IS. DISTRIBUTION STATEMENT
Release to Public
19. SECURITY CLASS (Thti Report)
Unclassified
21. NO. OF j*AGES
20. S1CURITV CLASS (Thhpaf*)
Unclassified
22. PRICE
CPA Form 2110-1 (••71)
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